WO3 Nanowires Enhance Molecular Alignment and Optical Anisotropy in Electrospun Nanocomposite Fibers: Implications for Hybrid Light-Emitting Systems

The molecular orientation in polymer fibers is investigated for the purpose of enhancing their optical properties through nanoscale control by nanowires mixed in electrospun solutions. A prototypical system, consisting of a conjugated polymer blended with polyvinylpyrrolidone, mixed with WO3 nanowires, is analyzed. A critical strain rate of the electrospinning jet is determined by theoretical modeling at which point the polymer network undergoes a stretch transition in the fiber direction, resulting in a high molecular orientation that is partially retained after solidification. Nearing a nanowire boundary, local adsorption of the polymer and hydrodynamic drag further enhance the molecular orientation. These theoretical predictions are supported by polarized scanning near-field optical microscopy experiments, where the dichroic ratio of the light transmitted by the fiber provides evidence of increased orientation nearby nanowires. The addition of nanowires to enhance molecular alignment in polymer fibers might consequently enhance properties such as photoluminescence quantum yield, polarized emission, and tailored energy migration, exploitable in light-emitting photonic and optoelectronic devices and for sensing applications.

. Thus, a segment of an entangled chain will elongate at a rate of .
In this, we assumed that the flow is uniaxial and sufficiently fast, so that both and are aligned with the direction of the flow. Averaged over the entire primitive length of the chain, The ≈ symbol denotes a scaling relationship, where constants of order unity are omitted. S2 We define the relative chain extension by = / max , where max = is the contour length of a chain having monomers of (Kuhn) length . Expressing Equation (S1) in terms of , and normalizing the tension force by / to make it dimensionless ( is Boltzmann constant and is absolute temperature), we get 1 where ≈ 2 2 / is the relaxation time of a stretched chain in a tube. This is Rouse relaxation time, 2 whose dependence on polymer and solution properties is calculated in section S2.
When the electrospinning jet reaches steady state, the velocity gradient is constant, = , and the time derivative of the relative extension is zero. Consequently, Equation (S2) reduces to ( ) −  where = / max and max is the length of a fully extended chain (contour length). Thus, max = 1/ 0 and 0 = 1. Substituting into the equation of ( ), and normalizing by the force at equilibrium (at rest), ( 0 ) ≅ 3 0 , we obtain the force function which is the function used in our study. ( ) is dimensionless as the force is normalized by / .
Another known form of the elastic force dependence on extension is the inverse Langevin function, which can be approximated by ≅ ( melt, which has a fixed value for a given polymer. 7 Thus, the initial extension of an entangled chain at rest is The exponent of is 0.54 for a good solvent and 0.67 for a θ-solvent.

S3. Calculation of chain elongation and orientation
In order to calculate the elongation and orientation parameters, we use Equation (7)  (S14) This is Equation (10) of the main text.
The explicit values of and 0 are not needed in this modeling, as the resulting orientation functions ( , 0 ) and ( , 0 ) are independent of them. Therefore, the orientation analysis applies for a general case of forces, which can account for entropic (elastic) energy due to stretching, as well as for excluded volume repulsive interaction energy to ensure avoidance of multiple lattice occupation. The latter could be incorporated as an approximate mean potential component in the force, [7][8][9] to represent the potential induced by far monomers and by neighboring chains, without impairing the validity of Equations (S11) and (S14) for a semi-dilute solution.
The orientation Equations (S11) and (S14) do not account for the radial strain rate of magnitude − /2 associated with the longitudinal strain rate , which exerts radial compression on the polymer chains (see section 3.5 in the main text). 10 We

S4. Scaling approximations for chain elongation and orientation
Approximations for the extension and orientation expressions (Equations (4), (5), (9) and (10) of the main text) are useful, as they provide simple scaling relationships with respect to the relative strain rate, / . The following approximations were obtained by series expansions at small 0 .
The chain extension scales as where is 3/ far from a boundary and 2/ near a boundary, and 0 is used near a boundary.
Far from the boundary of a filler, the orientation scales as